简述

先将前面两篇文章的代码重构一下，抽离共同函数到utils.py。

重构后结构：

ComputationGraphLinearNet.py：
使用计算图（forward、backward）求梯度构建的线性模型，代码不变；
代码：https://itsven.blog.csdn.net/article/details/141168288

NumericalGradientLinearNet.py:
使用数值微分求梯度构建的线性模型，代码不变；
代码：https://itsven.blog.csdn.net/article/details/141168156

utils.py：
测试数据构建；

main.py：
对上述代码整合运行；

测试结果

测试前提：
不考虑epoch、batch_size、learning_rate是否合理，只在这些参数相同情况下，比较数值微分求梯度、计算图求梯度两种方式构建的线性模型运算速度、运算结果的差异。

参数误差：

计算方式：相同参数的绝对值误差平均值，运行结果来看，误差很小。

for key in graphNet.params.keys():  diff = np.average(np.abs(graphNet.params[key] - numericalNet.params[key]))  params[key] = diff

时间差异：

epoch、batch_size=、learning_rate相同情况下，每次使用不同数据（数据大小5000），分别运行5次，明显计算图求梯度方法运算速度更快（时间：毫秒）。

完整代码

ComputationGraphLinearNet.py、NumericalGradientLinearNet.py 见：

使用计算图（forward、backward）求梯度构建的线性模型https://itsven.blog.csdn.net/article/details/141168288

使用数值微分求梯度构建的线性模型：https://itsven.blog.csdn.net/article/details/141168156

utils.py

import numpy as np  def build_data(weights, bias, num_examples):  x = np.random.randn(num_examples, len(weights))  y = x.dot(weights) + bias  # 给y加个噪声  y += np.random.rand(1)  return x, y  def data_iter(features, labels, batch_size):  num_examples = len(features)  # 按样本数量构造索引  indices = list(range(num_examples))  # 打乱索引数组  np.random.shuffle(indices)  for i in range(0, num_examples, batch_size):  batch_indices = np.array(indices[i:min(i + batch_size, num_examples)])  yield features[batch_indices], labels[batch_indices]

main.py

from ComputationGraphLinearNet import Network as GraphNet  
from NumericalGradientLinearNet import Network as NumericalNet  import utils  
import numpy as np  
import matplotlib.pyplot as plt  
import time  def numerical_test(x_train, y_train, batch_size, num_epochs):  numericalNet = NumericalNet(2, 1, 0.01)  loss_history = list()  for i in range(num_epochs):  for x, y in utils.data_iter(x_train, y_train, batch_size):  grads = numericalNet.numerical_gradient(x, y)  for key in grads:  numericalNet.params[key] -= learning_rate * grads[key]  running_loss = numericalNet.loss(x, y)  loss_history.append(running_loss)  print(f'最后一次损失值：{loss_history[-1]}')  print(f'预测参数: true_w1={numericalNet.params["w1"]}, true_b1={numericalNet.params["b1"]}')  return numericalNet  def graph_test(x_train, y_train, batch_size, num_epochs):  graphNet = GraphNet(2, 1, 0.01)  loss_history = list()  for i in range(num_epochs):  for x_batch, y_batch in utils.data_iter(x_train, y_train, batch_size):  grads = graphNet.gradient(x_batch, y_batch)  for key in grads:  graphNet.params[key] -= learning_rate * grads[key]  running_loss = graphNet.loss(x_batch, y_batch)  loss_history.append(running_loss)  print(f'最后一次损失值：{loss_history[-1]}')  print(f'预测参数: true_w1={graphNet.params["w1"]}, true_b1={graphNet.params["b1"]}')  return graphNet  if __name__ == '__main__':  test_num = 5  num_epochs = 2  batch_size = 50  learning_rate = 0.01  graph_time = list()  numerical_time = list()  error_list = list()  for i in range(test_num):  true_w1 = np.random.rand(2, 1)  true_b1 = np.random.rand(1)  x_train, y_train = utils.build_data(true_w1, true_b1, 5000)  print(f'\n----------------------------第{i+1}次')  print(f'第{i+1}次, 正确参数: true_w1={true_w1}, true_b1={true_b1}\n')  print("------------数值微分法：")  start = time.perf_counter()  numericalNet = numerical_test(x_train, y_train, batch_size, num_epochs)  end = time.perf_counter()  print(f"运行时间：{(end - start) * 1000}毫秒")  numerical_time.append((end - start) * 1000)  print("------------计算图法：")  start = time.perf_counter()  graphNet = graph_test(x_train, y_train, batch_size, num_epochs)  end = time.perf_counter()  print(f"运行时间：{(end - start) * 1000}毫秒")  graph_time.append((end - start) * 1000)  params = {}  for key in graphNet.params.keys():  diff = np.average(np.abs(graphNet.params[key] - numericalNet.params[key]))  params[key] = diff  error_list.append(params)  plt.title("数值微分、计算图两种求导速度差异", fontproperties="STSong")  plt.xlabel("nums")  plt.ylabel("time")  plt.xticks(range(0, test_num))  plt.plot(graph_time, linestyle='dotted', marker='o', label='graph_time')  plt.plot(numerical_time,  linestyle='dotted', marker='*', label='numerical_time')  plt.legend(loc='upper right')  plt.show()  for i in range(len(error_list)):  print(f'第{i+1}次运行, 各参数绝对误差的平均值{error_list[i]}', end="\n")